• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.447-469
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• 2018

Types (over parameters) in the theory of atomless random variable structures correspond precisely to (conditional) distributions in probability theory. Moreover, the logic (resp. metric) topology on the type space corresponds to the topology of weak (resp. strong) convergence of distributions. In this paper, we study metrics between types. We show that type spaces under $d^{\ast}-metric$ are isometric to Wasserstein spaces. Using optimal transport theory, two formulas for the metrics between types are given. Then, we give a new proof of an integral formula for the Wasserstein distance, and generalize some results in optimal transport theory.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.59-82
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• 2022

In this paper, we present a modified (improved) generalized M-iteration with the inertial technique for three quasi-nonexpansive multivalued mappings in a real Hilbert space. In addition, we obtain a weak convergence result under suitable conditions and the strong convergence result is achieved using the hybrid projection method with our modified generalized M-iteration. Finally, we apply our convergence results to certain optimization problem, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other improved iterative methods (modified SP-iterative scheme) in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.185-190
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• 2005

For the almost certainly convergent series $S_n$ of independent random variables the limiting behavior of tail series ${T_n}{\equiv}S-S_{n-1}$ is reviewed. More specifically, tail series strong laws of large number and tail series weak laws of large numbers will be introduced, and their relationship will be investigated. Then, the relationship will also be extended to the case of Banach space valued random elements, by investigating the duality between the limiting behavior of the tail series of random variables and that of random elements.

• The Mathematical Education
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• v.14 no.1
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• pp.19-21
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• 1975

약 위상과 강위상이 주어진 선형공간 E에서 수열의 약수렴과 강수렴에 관한 성질을 보조정리로하여 두 Banach공간 E와 F사이에 정의된 연속작용소 공간 L(E.F)에서 작용소열 { $T_{n}$ }이 T에 강수렴하기 위한 필요충분조건은 F가 Hilbert 공간일때는 { $T_{n}$ }이 T에 약수렴함과 동시에 실수열 (equation omitted)$T_{\chi}$ $n^{\chi}$(equation omitted)가 실수 (equation omitted)T$\chi$(equation omitted)에 수렴할 때이다.

• The Mathematical Education
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• v.31 no.2
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• pp.133-140
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• 1992

The problem of estimating a smooth distribution function F at a point $\tau$ based on randomly right censored data is treated under certain smoothness conditions on F . The asymptotic performance of a certain class of kernel estimators is compared to that of the Kap lan-Meier estimator of F($\tau$). It is shown that the .elative deficiency of the Kaplan-Meier estimate. of F($\tau$) with respect to the appropriately chosen kernel type estimate. tends to infinity as the sample size n increases to infinity. Strong uniform consistency and the weak convergence of the normalized process are also proved.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.3
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• pp.222-232
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• 2013

In recent years, 'technological fusion or convergence' has drawn a lot of attention of innovation researchers and governmental policy makers as the driving force of technological innovation and industrial growth. There are, however, few studies on the analysis of longitudinal trends of technological convergence and its comparison between global and national level. In this study, with the citation data of about 18 million articles, we analyzed 1) the growth of representative convergence research areas, 2) the convergence of citing patterns between research fields, and 3) the changing trend of diversity index of all research fields. We conclude that technological convergence in korea shows the relatively strong orientation to the combination of neighboring fields than that of heterogenous fields in comparison to global trend. In particular, the relatively weak activity of cognitive science and the low level of mutual exchange between arts/humanities/social sciences and natural/engineering sciences in Korea are emphasized.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.35-48
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• 2023

Let 𝔼 be a CAT(0) space and K be a nonempty closed convex subset of 𝔼. Let T : K → 𝓟(K) be a multimap such that F(T) ≠ ∅ and ℙ_T(x) = {y ∈ Tx : d(x, y) = d(x, Tx)}. Define sequence {x_n} by x_n+1 = (1 - α)𝜈_n⊕αw_n, y_n = (1 - β)u_n⊕βw_n, z_n = (1-γ)x_n⊕γu_n where α, β, γ ∈ [0; 1]; u_n ∈ ℙ_T (x_n); 𝜈_n ∈ ℙ_T (y_n) and w_n ∈ ℙ_T (z_n). (1) If ℙ_T is quasi-nonexpansive, then it is proved that {x_n} converges strongly to a fixed point of T. (2) If a multimap T satisfies Condition(I) and ℙ_T is quasi-nonexpansive, then {x_n} converges strongly to a fixed point of T. (3) Finally, we establish a weak convergence result. Our results extend and unify some of the related results in the literature.

• The Journal of the Korea Contents Association
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• v.6 no.5
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• pp.29-34
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• 2006

For the almost certainly convergent series $S_n=\sum_{i=1}^nV-i$ of independent random elements in Banach spaces, by investigating tail series laws of large numbers, the rate of convergence of the series $S_n$ to a random variable s is studied in this paper. More specifically, by studying the duality between the limiting behavior of the tail series $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$ of random variables and that of Banach space valued random elements, an alternative way of proving a result of the previous work, which establishes the equivalence between the tail series weak law of large numbers and a limit law, is provided in a Banach space setting.

• Asia-Pacific Journal of Business Venturing and Entrepreneurship
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• v.18 no.2
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• pp.53-66
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• 2023

Role models are also known to influence an individual's job or career choice. The positive effect of role models on entrepreneurship has already been revealed through many precious researches. It is said that people choose not only family members who are related by blood, such as parents, siblings, and relatives, but also acquaintances whom they have met through social relationships as role models. In this study, we divided into entrepreneurs with no role models other than themselves and entrepreneurs with role models. In addition, we classified parental siblings and relative role models as role models with strong ties, and acquaintance role models as role models with weak ties. We analyzed the differences in personal attributes, entrepreneurial orientation factors, and learning orientation between the entrepreneurs with role models and those without role models. Also, the differences in personal attributes, innovativeness, proactiveness, risk-taking propensity, and learning orientation between the entrepreneurs with strong ties role models and those with weak ties role models were examined. The empirical analysis results are as follows. First, it was found that the proportion of women entrepreneurs without role models is higher. Second, the entrepreneurs with role models with weak ties tend to run larger scale start-ups. Third, it was found that the entrepreneurs with role models of weak ties tend to have higher learning orientation. Fourth, gender shows the greatest influence on th absence or presence of role models. Fifth, it was found that learning orientation and startup size have the greatest influence on the decision of the role model with weak ties or that with strong ties.

• Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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• v.1 no.2
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• pp.119-124
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• 1997

Cloud streets were successfully simulated by numerical model (RAMS) including an isolated mountain near the coast, large sensible heat flux from the sea surface, uniform stratification and wind velocity with low Froude number (0.25) in the inflow boundary. The well developed cloud streets between a pair of convective rolls are simulated at a level of 1 km over the sea. The following five results were obtained: 1) For the formation of the pair of convective rolls, both strong static instability and a topographically induced mechanical disturbance are strongly required at the same time. 2) Strong sensible heat flux from the sea surface is the main energy source of the pair of convective rolls, and the buoyancy caused by condensation in the cloud is negligibly small. 3) The pair of convective rolls is a complex of two sub-rolls. One is the outer roll, which has a large radius, but weak circulation, and the other is the inner roll, which has a small radius, but strong circulation. The outer roll gathers a large amount of moisture by convergence in the lower marine boundary, and the inner roll transfers the convergent moisture to the upper boundary layer by strong upward motion between them. 4) The pair of inner rolls form the line-shaped cloud streets, and keep them narrow along the center-line of the domain. 5) Both by non-hydrostatic and by hydrostatic assumptions, cloud streets can be simulated. In our case, non-hydrostatic processes enhanced somewhat the formation of cloud streets. The horizontal size of the topography does not seem to be restricted to within the small scale where non-hydrostatic effects are important.